Meshfree PDE Solver on 1D Elliptic Manifold (GMLS/gRBF-FD)¶
- Task ID:
math.manifold_pde_meshfree - Domain:
math - Subdomain:
numerical_odes_pde - Status:
test - Tags:
meshfree,manifold,pde,laplace-beltrami,gmls,rbf-fd
Public Summary¶
This page is generated from task metadata and selected public-safe excerpts.
Example B1 Prompt Excerpt¶
# High-Order Meshfree PDE Solver on 1D Elliptic Manifold
> **Level B1**: Full algorithm description — provides complete implementation details.
## Problem
You are given a 1D elliptic curve embedded in ℝ²:
\[
\mathbf{x}(\theta) = (a\cos\theta, b\sin\theta), \quad \theta \in [0, 2\pi)
\]
with parameters \(a = {{ a }}, b = {{ b }}\). The Riemannian metric is \(g(\theta) = a^2\sin^2\theta + b^2\cos^2\theta\).
Notes¶
- This page is a generated site artifact.
- Higher-level prompt details and internal benchmark specifics may remain intentionally undisclosed.